%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET253-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:43 PM UTC 2026
% Result : Unsatisfiable 0.08s 5.46s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 16 unt; 2 def)
% Number of atoms : 60 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 21 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(restrict(x,y,z),cross_product(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f128,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f129,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f245,plain,
~ subclass(restrict(x,y,z),cross_product(y,z)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f262,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f129,f128]) ).
fof(f266,plain,
~ member(not_subclass_element(restrict(x,y,z),cross_product(y,z)),cross_product(y,z)),
inference(resolution,[status(thm)],[f117,f245]) ).
fof(f275,plain,
! [X0,X1] : ~ member(ordered_pair(X0,not_subclass_element(restrict(x,y,z),cross_product(y,z))),cross_product(X1,cross_product(y,z))),
inference(resolution,[status(thm)],[f266,f134]) ).
fof(f298,plain,
! [X0,X1] :
( ~ member(not_subclass_element(restrict(x,y,z),cross_product(y,z)),cross_product(y,z))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f275,f135]) ).
fof(f302,definition,
! [X0,X1] :
( sQ3_spl
<=> ~ member(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f303,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ member(X0,X1) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,definition,
( sQ4_spl
<=> member(not_subclass_element(restrict(x,y,z),cross_product(y,z)),cross_product(y,z)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ4_spl
| ~ member(not_subclass_element(restrict(x,y,z),cross_product(y,z)),cross_product(y,z)) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f298,f302,f305]) ).
fof(f311,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f262,f303]) ).
fof(f314,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f522,plain,
! [X0,X1,X2,X3] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f151,f142]) ).
fof(f2227,plain,
member(not_subclass_element(restrict(x,y,z),cross_product(y,z)),restrict(x,y,z)),
inference(resolution,[status(thm)],[f116,f245]) ).
fof(f4070,plain,
member(not_subclass_element(restrict(x,y,z),cross_product(y,z)),cross_product(y,z)),
inference(resolution,[status(thm)],[f522,f2227]) ).
fof(f4072,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4070,f307]) ).
fof(f4073,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f4072]) ).
fof(f4074,plain,
$false,
inference(sat_refutation,[status(thm)],[f308,f314,f4073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET253-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Mon Sep 21 05:02:44 UTC 2026
% 0.04/5.32 % CPUTime :
% 0.04/5.33 % Drodi V4.1.1
% 0.08/5.46 % Refutation found
% 0.08/5.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/5.48 % Elapsed time: 0.147741 seconds
% 0.08/5.48 % CPU time: 0.987184 seconds
% 0.08/5.48 % Total memory used: 136.122 MB
% 0.08/5.48 % Net memory used: 132.371 MB
%------------------------------------------------------------------------------